Abstract
We characterize certain function classes in terms of the remainder in the quadrature formula\(\int_{ - \infty }^\infty {f(x)dx = (\pi /\sigma )\sum\nolimits_{v = - \infty }^\infty {f(v\pi /\sigma ) + R_\sigma [f]} } \). In the process, we prove a generalization of the famous theorem of Paley and Wiener about entire functions of exponential type belonging toL 2 on the real line.
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Communicated by Paul Nevai.AMS classification: Primary 41A55; Secondary 30D15, 42A38, 46E10, 65D32.
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Dryanov, D.P., Rahman, Q.I. & Schmeisser, G. Converse theorems in the theory of approximate integration. Constr. Approx 6, 321–334 (1990). https://doi.org/10.1007/BF01890414
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DOI: https://doi.org/10.1007/BF01890414